服务系统中位相型分布的随机比较

本文运用应用概率中的随机占优研究位相型(PH)分布的随机比较问题,具体给出在一阶、二阶随机占优下比较两个离散PH分布或两个连续PH分布的充分条件及充分必要条件。研究表明,比较两个离散PH分布可变性的条件与比较两个连续PH分布可变性的条件不同,在二阶随机占优意义下比较两个连续PH分布的条件与均值无关,而比较两个离散PH分布的条件与均值有关。本文的结果可用于研究PH分布的最小变异系数问题和可变性问题,也可用于研究带有PH到达间隔或PH服务的排队系统中到达过程或服务时间可变性对系统队长或等待时间的影响。

Stochastic Comparison of Phase-type Distributions

In this paper, we analyze stochastic comparison of phase-type(PH)distributions by using stochastic dominance in applied probability, sufficient conditions and necessary and sufficient conditions for comparing two phase-type distributions under first and second degree stochastic dominance are provided. We prove that conditions to compare variabilities of two discrete phase-type distributions are different from those comparing variabilities of two continuous phase-type distributions. Conditions comparing two continuous phase-type distributions under second degree stochastic dominance are independent of their means, but conditions comparing two discrete phase-type distributions depend on their means. The results in this article can be applied to the problem for the minimization coefficient of variation and variabilities of phase-type distributions, and they can also be used to analyze the effect of variability of arrival process or service time on queue length or waiting time in queueing systems.